It makes no sense to send e-mails from DoNotReply@communityname.com accounts, nor to ask members not to reply to e-mails from the community.
If a member wants to reply, then you want him/her to be able to do so as quickly and easily as possible. You want your members to talk to you. If they have complaints, questions and suggestions, then you want to hear them. If they just want to chat, then you want to chat with them.
If the member doesn’t want to reply, then having an Do Not Reply e-mail address is irrelevant.
Most importantly, you should be encouraging replies, not discouraging them. If I receive a notification or an update, I want to be able to hit reply and contact whomever sent the e-mail.
Send e-mails from a clearly specified individual (Carol@communityname.com) with a call to action for people to reply.